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Unformatted text preview: First Order Logic (Predicate Calculus) CPS 170 Ronald Parr Limita<ons of Proposi<onal Logic •  Suppose you want to say: All humans are mortal •  For ~6B people, you would need ~6B proposi<ons •  Suppose you want to stay that (at least) one person has perfect pitch •  You would need a disjunc<on of ~6B proposi<ons •  There has to be a beMer way… 1 First Order Logic •  Proposi<onal logic is very restric<ve –  Can’t make global statements about objects in the world –  Workarounds tends to have very large KBs •  First order logic is more expressive –  Rela<ons, quan<ﬁca<on, func<ons –  but… inference is trickier First Order Syntax •  Sentences •  Atomic sentence predicate(term) •  Terms – func<ons, constants, variables •  Connec<ves •  Quan<ﬁers •  Constants •  Variables 2 Rela<ons •  Assert rela<onships between objects •  Examples –  Loves(Harry, Sally) –  Between(Canada, US, Mexico) •  Seman<cs –  Object and predicate names are mnemonic only –  Interpreta<on is imposed from outside –  O_en we imply the “expected” interpreta<on of predicates and objects with suggested names Func<ons •  Func<ons are specials cases of rela<ons •  Suppose R(x1,x2,…,xn,y) is such that for every value of x1,x2,…,xn there is a unique y •  Then R(x1,x2,…,xn) can be used as a shorthand for y –  Crossed(Right_leg_of(Ron), Le__leg_of(Ron)) •  Remember that the object iden<ﬁed by a func<on depends upon the interpreta<on 3 Quan<ﬁca<on •  For all objects in the world… ∀xhappy( x ) •  For at least one object in the world… € ∃xhappy( x ) € Examples •  Eve...
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